Timeline for What exactly is the precision of an estimate?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2017 at 17:23 | vote | accept | amarsh | ||
| Oct 23, 2017 at 22:20 | comment | added | amarsh | @whuber Well, the true motivation was trying to determine if I should ask for a regrade of that question (which I am allowed to do). The TA's grade the mid-terms first based on the answer key and then the professor evaluates the regrade requests. But I wanted to know the actual statistical meaning of precise before doing so, because we really weren't given one in lecture nor in the textbook "Econometric Analysis" by Greene (at least, not what we've covered so far). | |
| Oct 23, 2017 at 22:18 | comment | added | dimitriy | @whuber My question was about your concern regarding the units of the parameters in multivariate regression. The outcome is the same and regressor in question is the same in both models, so the they seem comparable to me. I meant to write "isn't" instead of "it's". | |
| Oct 23, 2017 at 22:12 | comment | added | whuber♦ | @Dimitriy Would you mean the response? I'm discussing only a single multiple regression, such as GDP against population size and date, applied to a single dataset. I guess the point I'm beating around concerns whether "precision" is intended in the sense of "offering well-estimated information about the value of a coefficient" compared to "offering well-estimated information about the conditional expectations of a response." This was prompted by my (perhaps misguided) effort to make some sense, any sense, of an answer key in which "precision" was interpreted in terms of "significance." | |
| Oct 23, 2017 at 22:03 | comment | added | dimitriy | @whuber It's the regressor the same in both equations? | |
| Oct 23, 2017 at 21:34 | comment | added | whuber♦ | "Relative" doesn't mean all comparisons are meaningful. If, for instance, I have estimated a mass to the nearest kilogram and a height to the nearest meter, which is more precise? Or in a multiple regression, if one parameter estimate is in dollars per capita and it's estimated to within about 10 percent and another parameter estimate is dollars per year and it's estimated to within 1 percent, which is more precise for this regression model? You just can't tell from such information. | |
| Oct 23, 2017 at 21:31 | comment | added | amarsh | @whuber I understand your standardization comment. However, given what we were, I figured comparing the standard errors between the two was the best way to answer the question. Especially since (I thought) precision was a relative term (though I may be confusing that with efficiency). | |
| Oct 23, 2017 at 21:31 | comment | added | whuber♦ | Thank you for the full quotation. We may infer from it that its author thinks of "precision" as being "degree of one's ability to distinguish a quantity from zero." For instance, a measurement of an adult human's height to the nearest meter would be considered "precise" in this sense. It seems safe to conclude that this meaning of "precision" differs from how most people--statisticians and non-statisticians alike--conceive of this word. | |
| Oct 23, 2017 at 21:27 | answer | added | AdamO | timeline score: 0 | |
| Oct 23, 2017 at 21:20 | comment | added | dimitriy | Precision is the accuracy of an estimator as measured by the inverse of its variance. The standard errors are the square root of that variance. | |
| Oct 23, 2017 at 21:20 | comment | added | amarsh | I don't think I misquoted it, but here is the exact wording (substituting in my toy example): "Yes, the effect of $b_{12}$ on $y$ in Regression #2 is fairly precisely estimated. The t ratio, which is the ratio of the Coef. divided by its Std. Err. is 2.94, indicates a reasonable amount of precision in the estimation of this coefficient, which is estimated to be .3793769." | |
| Oct 23, 2017 at 21:18 | comment | added | whuber♦ | (1) I hope you have somehow misquoted or incorrectly summarized the answer key, because it's a little mind-boggling to see precision confused with statistical significance! (2) Unless your $b_{ij}$ are coefficients of standardized variables, what sense does it make to compare the standard error of one to the standard error of another? | |
| Oct 23, 2017 at 21:14 | history | asked | amarsh | CC BY-SA 3.0 |